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Project-declaredLean 4.32.0 ยท mathlib@81a5d257c8e4

Time Contract mem center

FieldSpecification.WickAlgebra.timeContract_mem_center

Plain-language statement

For a field specification ๐“•, and ฯ† and ฯˆ elements of ๐“•.FieldOp, then timeContract ฯ† ฯˆ is in the center of ๐“•.WickAlgebra.

Exact Lean statement

lemma timeContract_mem_center (ฯ† ฯˆ : ๐“•.FieldOp) :
    timeContract ฯ† ฯˆ โˆˆ Subalgebra.center โ„‚ ๐“•.WickAlgebra

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
lemma timeContract_mem_center (ฯ† ฯˆ : ๐“•.FieldOp) :    timeContract ฯ† ฯˆ โˆˆ Subalgebra.center โ„‚ ๐“•.WickAlgebra := by  by_cases h : timeOrderRel ฯ† ฯˆ  ยท rw [timeContract_of_timeOrderRel _ _ h]    exact superCommute_anPart_ofFieldOp_mem_center ฯ† ฯˆ  ยท rw [timeContract_of_not_timeOrderRel _ _ h]    refine Subalgebra.smul_mem (Subalgebra.center โ„‚ _) ?_ ๐“ข(๐“• |>โ‚› ฯ†, ๐“• |>โ‚› ฯˆ)    rw [timeContract_of_timeOrderRel]    exact superCommute_anPart_ofFieldOp_mem_center _ _    have h1 := Std.Total.total (r := ๐“•.timeOrderRel) ฯ† ฯˆ    simp_all
Project
Physlib
License
Apache-2.0
Commit
dd43e9e65791
Source
Physlib/QFT/PerturbationTheory/WickAlgebra/TimeContraction.lean:85-95

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Related declarations

Project-declaredLean 4.32.0

Adiabatic relation log

adiabatic_relation_log

Plain-language statement

Adiabatic relation in logarithmic form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then c * log (Ua/Ub) + log (Va/Vb) = 0.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Adiabatic relation Ua Ub Va Vb

adiabatic_relation_UaUbVaVb

Plain-language statement

Adiabatic relation in product form: If S(Ua,Va,N) = S(Ub,Vb,N) with N fixed, then (Ua/Ub)^c * (Va/Vb) = 1.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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